Compatibility of Cyclic Causal Structures with Spacetime in General
Theories with Free Interventions
- URL: http://arxiv.org/abs/2211.03593v3
- Date: Mon, 24 Apr 2023 20:14:33 GMT
- Title: Compatibility of Cyclic Causal Structures with Spacetime in General
Theories with Free Interventions
- Authors: Maarten Grothus
- Abstract summary: We show the possibility of operationally detectable causal loops embedded in (1+1)-Minkowski spacetime without superluminal signalling.
We establish new properties of HO affects relations and apply them to infer causal structures.
We study the embedding of information-theoretic causal structures into partially ordered spacetimes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: By relating and ordering events, causality constitutes a pivotal feature of
our world. On the one hand, there are information-theoretic notions of
causality defined in terms of the information processing ability of agents and
on the other hand, there are relativistic notions of causality tied to a
spacetime. In this thesis, we improve upon a framework introduced by V.
Vilasini and R. Colbeck in PRA, 106, 032204 (2022) and PRL, 129, 110401 (2022)
for connecting these notions, where the possibility of operationally detectable
causal loops embedded in (1+1)-Minkowski spacetime without superluminal
signalling was demonstrated. In the first part, we take the
information-theoretic point of view, where the concept of higher-order (HO)
affects relations was proposed to generically model signalling in the presence
of cyclic, fine-tuned and non-classical causal influences. We establish new
properties of HO affects relations and apply them to infer causal structures.
We then demonstrate a complete and constructive way to detect causal loops from
a set of HO affects relations. In the second part, we study the embedding of
information-theoretic causal structures into partially ordered spacetimes. We
propose stability conditions on the spacetime embedding to rule out a class of
operationally detectable loops that cannot be ruled out by the principle of
no-signalling (outside the relativistic future) alone. We then propose novel
order-theoretic properties that we conjecture to hold in Minkowski spacetime
with $d \geq 2$ spatial dimensions. This would imply that in contrast to
(1+1)-Minkowski spacetime, in higher dimensions, the no-signalling principle is
indeed sufficient for ruling out this class of loops. Finally, we introduce a
relation which allows for causal inference through knowledge about the absence
of signalling relations and we relate it to novel order-theoretic features of
spacetime.
Related papers
- New Rules for Causal Identification with Background Knowledge [59.733125324672656]
We propose two novel rules for incorporating BK, which offer a new perspective to the open problem.
We show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data.
arXiv Detail & Related papers (2024-07-21T20:21:21Z) - Characterizing Signalling: Connections between Causal Inference and
Space-time Geometry [0.0]
Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic.
We use a framework introduced in PRA, 106, 032204 (2022), which formally connects these two notions in general physical theories.
We study the embedding of information-theoretic causal models in space-time without violating relativistic principles.
arXiv Detail & Related papers (2024-03-01T19:00:45Z) - A causal modelling analysis of Bell scenarios in space-time:
implications of jamming non-local correlations for relativistic causality
principles [1.0878040851638]
Bell scenarios involve space-like separated measurements made by multiple parties.
Non-signalling constraints have been proposed, which permit a class of post-quantum theories known as jamming non-local theories.
We show that any theory that generates jamming correlations in a Bell scenario must necessarily do so through causal fine-tuning and by means of superluminal causal influences.
arXiv Detail & Related papers (2023-11-30T11:17:49Z) - A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality.
Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
arXiv Detail & Related papers (2023-05-19T13:15:48Z) - Impossibility of superluminal signalling in Minkowski space-time does
not rule out causal loops [2.0305676256390934]
We show the possibility of causal loops that can be embedded in a Minkowski space-time without leading to superluminal signalling.
The existence of such loops in the given space-time could in principle be operationally verified using interventions.
arXiv Detail & Related papers (2022-06-26T14:15:56Z) - Embedding cyclic causal structures in acyclic space-times: no-go results
for indefinite causality [2.1030878979833467]
Causality can be defined in terms of space-time or based on information-theoretic structures, which correspond to very different notions of causation.
We develop a framework that disentangles the two causality notions and formalises their relations.
Our work offers concrete insights on the operational meaning of indefinite causality, both within and beyond the context of a fixed space-time.
arXiv Detail & Related papers (2022-03-21T18:12:44Z) - A general framework for cyclic and fine-tuned causal models and their
compatibility with space-time [2.0305676256390934]
Causal modelling is a tool for generating causal explanations of observed correlations.
Existing frameworks for quantum causality tend to focus on acyclic causal structures that are not fine-tuned.
Cyclist causal models can be used to model physical processes involving feedback.
Cyclist causal models may also be relevant in exotic solutions of general relativity.
arXiv Detail & Related papers (2021-09-24T18:00:08Z) - Interplay between transport and quantum coherences in free fermionic
systems [58.720142291102135]
We study the quench dynamics in free fermionic systems.
In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
arXiv Detail & Related papers (2021-03-24T17:47:53Z) - Causal Expectation-Maximisation [70.45873402967297]
We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs.
We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables.
We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
arXiv Detail & Related papers (2020-11-04T10:25:13Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z) - Dynamical solitons and boson fractionalization in cold-atom topological
insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities.
We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors.
Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.